What is the domain of sec(2x-3pi) ?

The domain of sec(2x-3pi) is pin<= x< pi/4+pin\lor pi/4+pin<x<(3pi)/4+pin\lor (3pi)/4+pin<x<pi+pin

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domain of sec(2x-3pi)

domain

sec (2 x - 3 π)

πn \leq x < \frac{π}{4} + πn or \frac{π}{4} + πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

Interval Notation

[πn, \frac{π}{4} + πn) \cup (\frac{π}{4} + πn, \frac{3 π}{4} + πn) \cup (\frac{3 π}{4} + πn, π + πn)

Solution steps

Take the denominator(s) of

sec (2 x - 3 π)

and compare to zero:

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

Periodicity of

sec (2 x - 3 π) : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn \leq x < \frac{π}{4} + πn or \frac{π}{4} + πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

What is the domain of sec(2x-3pi) ?
The domain of sec(2x-3pi) is pin<= x< pi/4+pin\lor pi/4+pin<x<(3pi)/4+pin\lor (3pi)/4+pin<x<pi+pin